Question:medium

If \( f(x) = \int_0^x t(\sin x - \sin t)dt \) then :

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Always extract terms containing 'x' outside the integral before differentiating. If you see a term in the derivative that matches an earlier order derivative, substitute it immediately to find the required differential equation. \

Updated On: Apr 19, 2026

\( f'''(x) - f''(x) = \cos x - 2x\sin x \)
\( f'''(x) + f'(x) = \cos x - 2x\sin x \)
\( f'''(x) + f''(x) = \sin x \)
\( f'''(x) + f''(x) - f'(x) = \cos x \)

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The Correct Option is B

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If \( f(x) = \int_0^x t(\sin x - \sin t)dt \) then :

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The Correct Option is B

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